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I check, intending to raise CO's bet

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I think this was your mistake. You don't really have a reason to expect the CO to bet. You 3-bet preflop, and this is a scary board. It would also be terrible to give a free card here. You gotta bet this.

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Yes.

It is very important to realize that the combination of factors:

1. You three-bet pre-flop and didn't get capped.
2. The board is about as scary with draws as possible.

Means that it's very, very difficult to assume that a bet is coming from any one specific place.

Since you can't assume that you'll be able to manipulate the pot by raising a specific bettor, and because the board is crazy and you'll get action, and because you have a big hand, just bet.

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Totally. someone will be megastoked to get a free card here. I think letting them have that chance, however small, is a mistake is a big pot like this one.